Receiver with prefiltering for discrete fourier transform-spread-orthogonal frequency division multiplexing (DFT-S-OFDM) based systems

ABSTRACT

A receiver for discrete Fourier transform-spread-orthogonal frequency division multiplexing (DFT-S-OFDM) based systems, including a prefilter for received signal codeword(s); and a log-likelihood ratio LLR module responsive to the prefilter; wherein the prefilter includes a pairing and whitening module that based on channel estimates and data rate enables the LLR module to perform either a Serial-In-Serial-Out (SISO) based log likelihood ratio processing of an output from the paring and whitening module or a two-symbol max-log soft output demodulator (MLSD) based log likelihood ratio processing of an output from the pairing and whitening module.

This application claims the benefit of U.S. Provisional Application No.61/045,298, entitled “Efficient receiver Algorithms for DFT-SpreadSpectrum OFDM Systems”, filed on Apr. 16, 2008, the contents of which isincorporated by reference herein.

BACKGROUND OF THE INVENTION

The present invention relates generally to wireless communications, andmore particularly, to a receiver for DFT-Spread MIMO-OFDM systems.

Referring to the diagram in FIG. 1, each mobile (or source) transmitsits signal using the DFT-S-OFDM technique. The destination or basestation receives signals from several mobiles possibly overlapping intime and frequency and has to decode the signal of each mobile.

Discrete Fourier Transform-spread-Orthogonal Frequency Division MultipleAccess (DFT-spread-OFDMA or DFT-S-OFDMA) has emerged as the preferreduplink air interface for the next generation cellular systems such asthe 3GPP LTE. The main advantage of this multiple access technique isthat it results in considerably lower envelope fluctuations in thesignal waveform transmitted by each user and consequently lowerpeak-to-average-power ratio (PAPR) compared to the classical OFDMAtechnique. A lower PAPR in turn implies a smaller power back off at theuser terminal and hence an improved coverage for the cellular system.Another key technology that will be employed in the upcoming cellularsystems is the utilization of antenna arrays at the base station (a.k.aNode-B) and possibly at the user equipment (UE). Multiple antennas whenused in point-to-point or multipoint-to-point systems have been shown intheory to result insubstantial capacity improvements, provided that theenvironment is sufficiently rich in multipath components. However, inpractice the capacity improvement obtained by using multiple antennas atthe UEs in the uplink can be much smaller due to the fact that multipleantennas will have to be accommodated in the limited space available atthe UE, which will result in correlated channel responses that are notconducive to high rate communications. Moreover, installing multiplepower amplifiers in each UE is currently deemed impractical based oncost considerations by many vendors.

A promising scheme, also adopted in 3GPP LTE, which circumvents thesetwo issues is the space-division multiple-access (SDMA) scheme which issometimes referred to as the virtual multiple-input-multiple-output(MIMO) scheme. In SDMA multiple single-antenna users are scheduled overthe same frequency and time resource block in order to boost the systemthroughput. Since different users are geographically separated, theirchannel responses seen at the base-station antenna array will beindependent and hence capable of supporting high rate communications.Henceforth, the DFT-S-OFDM based uplink employing SDMA will be referredto as the DFT-S-OFDM-SDMA uplink.

In DFT-S-OFDM systems, which encompass both DFT-S-OFDMA andDFT-S-OFDM-SDMA, as a consequence of the DFT spreading operation at thetransmitter, the signal arrives at the base-station with substantialintersymbol interference and the received sufficient statistics can bemodeled as the channel output of a large MIMO system. The conventionalreceiver technique involves tone-by-tone single-tap equalizationfollowed by an inverse DFT operation. While such a simple receiversuffices for the single-user case in the low-rate regime when there isenough receive diversity and where the available frequency diversity canbe garnered by the underlying outer code, it results in degradedperformance at higher rates as well as with SDMA.

Unfortunately, unlike classical OFDMA, the large dimension of theequivalent MIMO model in DFT-S-OFDMA does not allow us to leverage thesphere decoder which has an exponential complexity in the problemdimension. Furthermore, the stringent complexity constraints inpractical systems also rule out the near-optimal MIMO receiversdeveloped for the narrowband channels. Other promising equalizers forthe DFT-S-OFDM systems are the decision feedback equalizers (DFE), inparticular the hybrid DFE, where the feedforward filter is realized inthe frequency domain and the feedback filter is realized in the timedomain, and the iterative block DFE with soft decision feedback that hasbeen proposed by others, where even the cancelation is performed in thefrequency domain. However, even the DFE whose iterative process does notinclude decoding the outer code is substantially more complex and hashigher latency especially in the SDMA case, than the conventionalreceiver.

Accordingly, there is a need for a receiver at the destination or basestation that can receive and decode multiple wireless signalsoverlapping in time and frequency in a manner that overcomes thelimitations of the conventional receiver techniques discussed above.

SUMMARY OF THE INVENTION

In accordance with the invention, there is provided a receiver fordiscrete fourier transform-spread-orthogonal frequency divisionmultiplexing (DFT-S-OFDM) based systems, including a prefilter forreceived signal codeword(s); and a log-likelihood ratio LLR moduleresponsive to the prefilter; wherein the prefilter includes a pairingand whitening module that based on channel estimates and data rateenables the LLR module to perform either a Serial-In-Serial-Out (SISO)based log likelihood ratio processing of an output from the pairing andwhitening module or a two-symbol max-log soft demodulator (MLSD) basedlog likelihood ratio processing of an output from the pairing andwhitening module. In a preferred embodiment, the prefilter furtherincludes a per-tone equalizer for the received signal codeword(s) and aninverse discrete Fourier transform IDFT module responsive to theequalizer, with the pairing and whitening module being responsive to theIDFT.

BRIEF DESCRIPTION OF DRAWINGS

These and other advantages of the invention will be apparent to those ofordinary skill in the art by reference to the following detaileddescription and the accompanying drawings.

FIG. 1 is a diagram of an exemplary wireless network, with multiplemobile signal sources 11-13 transmitting to a destination base-station10, in which the inventive receiver can be employed.

FIG. 2 is diagram of a two-symbol MLSD DFT-S-OFDM receiver in accordancewith the invention.

FIG. 3 is a diagram of the prefilter, shown in the receiver diagram ofFIG. 2, demodulating a single signal codeword, in accordance with theinvention.

FIG. 4 is a diagram of the prefilter, shown in the receiver diagram ofFIG. 2, demodulating multiple signal codewords, in accordance with theinvention.

DETAILED DESCRIPTION

The invention is directed to a more powerful receiver for DFT-spreadOFDM systems that includes an efficient linear pre-filter and atwo-symbol max-log soft-output demodulator. The proposed inventivereceiver can be applied to both single user per resource block (RB)(DFT-S-OFDMA) and multiple users per RB (DFT-S-OFDM-SDMA) systems and itoffers significant performance gains over the conventional method,especially in the high-rate regime, with little attendant increase incomputational complexity.

Referring now to FIG. 2 there is shown an exemplary two-symbol MLSDDFT-S-OFDM-SDMA Receiver employing the inventive pre-filteringprocessing. Transmitted data symbols are received at the pre-filterprocessor 14 and then sent to the two-symbol max-log soft-outputdemodulator (MLSD) 15 which outputs log Likelihood Ratios (LLR)corresponding to the user equipments 16. The prefilter 14 structure isdepicted in FIG. 3 demodulating a single user signal codeword anddemodulating multiple signal codewords in FIG. 4.

For understanding of the invention and the block diagrams of FIG. 3 andFIG. 4, we present the underlying signal analysis to arrive at theinventive signal receiving. Parenthetical numbers referencing particularsignal processes are referred to again when discussing correspondingreceiver processes.

We derive a simple receiver for the DFT-S-OFDM-SDMA uplink. Forconvenience we consider SDMA with two UEs but the receiver can beextended to more than two UEs as well as the DFT-S-OFDMA uplink withonly one UE.

Receivers for DFT-S-OFDM Based Systems 1-1.4

1 DFT-S-OFDM-SDMA Receivers

We assume that there are two UEs and for the m-th subcarrier (tone) then_(R)×1 channel response vector of the k-th UE is h_(m) ^((k))ε

^(n) ^(R) and the DFT-spread symbol is x_(m) ^((k)), k=1, 2. Thereceived signal vector on the m-th tone is given by

$\begin{matrix}{{{y_{m} = {{H_{m}x_{m}} + n_{m}}},{where}}{H_{m}\overset{\bigtriangleup}{=}{{\left\lbrack {h_{m}^{(1)},h_{m}^{(2)}} \right\rbrack\mspace{14mu}{and}\mspace{14mu} x_{m}}\overset{\bigtriangleup}{=}{\left\lbrack {x_{m}^{(1)},x_{m}^{(2)}} \right\rbrack^{T}.}}}} & (1)\end{matrix}$The noise vector n_(m) is spatially uncorrelated and satisfiesE[n_(m)n_(m) ^(†)]=I. We define s^((k))=[s₁ ^((k)), s₂ ^((k)), . . . ,s_(M) ^((k))]^(T) for k=1, 2, where {s_(m) ^((k))} are QAM symbolsnormalized to have unit average energy and let x^((k))=[x₁ ^((k)), x₂^((k)), . . . , x_(M) ^((k))]^(T)=Fs^((k)), where F is the M×M DFTmatrix. We can now write the received signal over all the M tones in thematrix form as

$\begin{matrix}{{{y = {{{\left\lbrack {H^{(1)},H^{(2)}} \right\rbrack\begin{bmatrix}x^{(1)} \\x^{(2)}\end{bmatrix}} + n} = {{\left\lbrack {{H^{(1)}F},{H^{(2)}F}} \right\rbrack\begin{bmatrix}s^{(1)} \\s^{(2)}\end{bmatrix}} + n}}},{where}}{{y\overset{\bigtriangleup}{=}{\left\lbrack {y_{1}^{T},y_{2}^{T},\ldots\mspace{14mu},y_{M}^{T}} \right\rbrack^{T} \in {\mathbb{C}}^{n_{R}M}}},{{{and}\mspace{14mu} H^{(k)}}\overset{\bigtriangleup}{=}{{{diag}\left( {h_{1}^{(k)},{\ldots\mspace{14mu} h_{M}^{(k)}}} \right)} \in {{\mathbb{C}}^{n_{R}M \times M}.}}}}} & (2)\end{matrix}$1.1 Conventional Linear MMSE (LMMSE) ReceiverThe linear MMSE estimate of x_(m) ^((k)), k=1, 2, based on y_(m) in (1)is given by¹

$\begin{matrix}{{\begin{bmatrix}{\hat{x}}_{m}^{(1)} \\{\hat{x}}_{m}^{(2)}\end{bmatrix} = {{{H_{m}^{\dagger}\left( {I + {H_{m}H_{m}^{\dagger}}} \right)}^{- 1}y_{m}} = {\left( {I + {H_{m}^{\dagger}H_{m}}} \right)^{- 1}H_{m}^{\dagger}y_{m}}}},{m = 1},\ldots\mspace{14mu},{M.}} & (3)\end{matrix}$Defining {circumflex over (x)}^((k))=[{circumflex over (x)}₁ ^((k)), . .. , {circumflex over (x)}_(M) ^((k))]^(T) and applying the inverse DFTon {circumflex over (x)}^((k)), we obtain

$\begin{matrix}{{\hat{s}}^{(k)}\overset{\bigtriangleup}{=}{F^{\dagger}{\hat{x}}^{(k)}}} & (4) \\{{{\hat{s}}_{i}^{(k)} = {{\alpha^{(k)}s_{i}^{(k)}} + v_{i}^{(k)}}},{i = 1},\ldots\mspace{14mu},M,} & (5) \\{{{{with}\mspace{14mu}\alpha^{(k)}} = {\frac{1}{M}{\sum\limits_{m = 1}^{M}d_{m}^{(k)}}}}{{{and}\mspace{14mu} d_{m}^{(k)}} = {{h_{m}^{{(k)}\dagger}\left( {{H_{m}H_{m}^{\dagger}} + I} \right)}^{- 1}h_{m}^{(k)}}}} & (6)\end{matrix}$Then, (4) can be simplified as

$\begin{matrix}{{{\hat{s}}_{i}^{(k)} = {{\alpha^{(k)}s_{i}^{(k)}} + v_{i}^{(k)}}},{i = 1},\ldots\mspace{14mu},M,{with}} & (5) \\{\alpha^{(k)} = {{\frac{1}{M}{\sum\limits_{m = 1}^{M}{d_{m}^{(k)}\mspace{14mu}{and}{\mspace{14mu}\;}d_{m}^{(k)}}}} = {{h_{m}^{{(k)}\dagger}\left( {{H_{m}H_{m}^{\dagger}} + I} \right)}^{- 1}h_{m}^{(k)}}}} & (6)\end{matrix}$where v_(i) ^((k)) contains the residual interference and noise, withvariance

[|v _(i) ^((k))|²]=α^((k))(1−α^((k))).  (7)1.2 New SDMA ReceiverAll operations up-to equation (4) are same as the conventional LMMSEreceiver. We thus obtain

${\hat{s}}^{(1)}\overset{\bigtriangleup}{=}{{F^{\dagger}{\hat{x}}^{(1)}\mspace{14mu}{and}\mspace{14mu}{\hat{s}}^{(2)}}\overset{\bigtriangleup}{=}{F^{\dagger}{{\hat{x}}^{(2)}.}}}$Let us expand ŝ⁽¹⁾=[ŝ₁ ⁽¹⁾, . . . , ŝ_(M) ⁽¹⁾]^(T) and ŝ⁽²⁾=[ŝ₁ ⁽²⁾, . .. , ŝ_(M) ⁽²⁾]^(T). Next, form the pairs ŝ_(m)=[ŝ_(m) ⁽¹⁾, ŝ_(m)⁽²⁾]^(T) for 1≦m≦M.

We will demodulate each one of the M pairs using a two-symbol max-logdemodulator. Before that we need to do a “noise-whitening” operation oneach of the M pairs. To do this, we determine

$C = {\frac{1}{M}{\sum\limits_{m = 1}^{M}{\left( {I + {H_{m}^{\dagger}H_{m}}} \right)^{- 1}.}}}$Note that the terms (I+H_(m) ^(†)H_(m))⁻¹, 1≦m≦M are computed in theLMMSE filter so they need not be re-computed. Next, we compute the 2×2matrix Qε

^(2×2) using the Cholesky decompositionQQ ^(†)=(I−C)C  (8)and then determine

${z_{m}\overset{\bigtriangleup}{=}{Q^{- 1}{\hat{s}}_{m}}},$1≦m≦M. z_(m)ε

^(2×1) permits the expansion

$\begin{matrix}{{z_{m} = {{\underset{\underset{T}{︸}}{Q^{- 1}\left( {I - C} \right)}s_{m}} + {\overset{\Cup}{n}}_{m}}},{1 \leq m \leq M},} & (9)\end{matrix}$with Tε

^(2×2), s_(m)=[s_(m) ⁽¹⁾, s_(m) ⁽²⁾]^(T) and

[{hacek over (n)}_(m){hacek over (n)}_(m) ^(†)]=I. The two symbols ins_(m) can now be jointly demodulated using the two-symbol max-logdemodulator on z_(m) for 1≦m≦M.(.)^(†) denotes the conjugate transpose operator.1.3 New SDMA Receiver with Improved PairingAll operations up-to equation (4) are same as the conventional LMMSEreceiver. We thus obtain

${\hat{s}}^{(1)}\overset{\bigtriangleup}{=}{{F^{\dagger}{\hat{x}}^{(1)}\mspace{14mu}{and}\mspace{14mu}{\hat{s}}^{(2)}}\overset{\bigtriangleup}{=}{F^{\dagger}{{\hat{x}}^{(2)}.}}}$Let us expand ŝ⁽¹⁾=[ŝ₁ ⁽¹⁾, . . . , ŝ_(M) ⁽¹⁾]^(T) and ŝ⁽²⁾=[ŝ₁ ⁽²⁾, . .. , ŝ_(M) ⁽²⁾]^(T). Suppose we form the pairs ŝ_(m,q)=[ŝ_(m) ⁽¹⁾,ŝ_([m+q]) ⁽²⁾]^(T) for 1≦m≦M and any given q: 0≦q≦M−1 and where[m+q]=(m+q−1)mod(M)+1. Then we determine the matrix X(q) such that

$\begin{matrix}{{{I - {X(q)}} = {\frac{1}{M}\begin{bmatrix}{\sum\limits_{k = 1}^{M}{h_{k}^{{(1)}\dagger}R_{k}^{- 1}h_{k}^{(1)}}} & {\sum\limits_{k = 1}^{M}{h_{k}^{{(1)}\dagger}R_{k}^{- 1}h_{k}^{(2)}{\exp\left( {{- j}\; 2\;\pi\;{{q\left( {k - 1} \right)}/M}} \right)}}} \\{\sum\limits_{k = 1}^{M}{h_{k}^{{(2)}\dagger}R_{k}^{- 1}h_{k}^{(1)}{\exp\left( {j\; 2\;\pi\;{{q\left( {k - 1} \right)}/M}} \right)}}} & {\sum\limits_{k = 1}^{M}{h_{k}^{{(2)}\dagger}R_{k}^{- 1}h_{k}^{(2)}}}\end{bmatrix}}},} & (10)\end{matrix}$where R_(k)=I+H_(k)H_(k) ^(†). Please note that the pairing used inSection 1.2 always uses q=0. Next, we compute the 2×2 matrix Q(q)ε

^(2×2) using the Cholesky decompositionQ(q)Q(q)^(\)=(I−X(q))X(q)  (11)and then determine

${z_{m,q}\overset{\bigtriangleup}{=}{{Q(q)}^{- 1}{\hat{s}}_{m,q}}},$1≦m≦M. z_(m,q)ε

^(2×1) permits the expansion

$\begin{matrix}{{z_{m,q} = {{\underset{\underset{T{(q)}}{︸}}{{Q(q)}^{- 1}\left( {I - {X(q)}} \right)}s_{m,q}} + {\overset{\Cup}{n}}_{m,q}}},{1 \leq m \leq M},} & (12)\end{matrix}$with T(q)ε

^(2×2), s_(m,q)=[s_(m) ⁽¹⁾, s_([m+q]) ⁽²⁾]^(T) and

[{hacek over (n)}_(m,q){hacek over (n)}_(m,q) ^(†)]=I. The two symbolsin s_(m,q) can now be jointly demodulated using the two-symbol max-logdemodulator on z_(m,q) for 1≦m≦M.

To determine the best q (or equivalently the best pair (m, [m+q])) wecan use the capacity metric on the model in (12) and determine asuitable {circumflex over (q)} as

$\begin{matrix}\begin{matrix}{{\arg\;{\max\limits_{0 \leq q \leq {M - 1}}{\det\left( {I + {{T(q)}^{\dagger}{T(q)}}} \right)}}} = {\arg\;{\max\limits_{0 \leq q \leq {M - 1}}{\det\left( {X(q)}^{- 1} \right)}}}} \\{= {\arg\;{\min\limits_{0 \leq q \leq {M - 1}}{{\det\left( {X(q)} \right)}.}}}}\end{matrix} & (13)\end{matrix}$Thus, we can equivalently first determine the vectorr=F[h ₁ ^((1)†) R ₁ ⁻¹ h ₁ ⁽²⁾ , . . . , h _(M) ^((1)†) R _(M) ⁻¹ h _(M)⁽²⁾]^(T)  (14)and compute {circumflex over (q)} as

$\begin{matrix}{\hat{q} = {{\arg\;{\max\limits_{1 \leq k \leq M}\left\{ {r_{k}} \right\}}} - 1.}} & (15)\end{matrix}$1.4 New OFDMA Receiver with Improved PairingWe only demodulate the symbols of a particular user of interest. Supposefor the m-th subcarrier (tone) the n_(R)×1 channel response vector ofthe UE is h_(m)ε

^(n) ^(R) and the DFT-spread symbol is x_(m). The received signal vectoron the m-th tone is given byy _(m) =h _(m) x _(m) +n _(m),  (16)where the noise vector n_(m) satisfies E[n_(m)n_(m) ^(†)]=S_(m). Wedefine R_(m)=h_(m)h_(m) ^(†)+S_(m) for 1≦m≦M and s=[s₁, s₂, . . . ,s_(M)]^(T), where {s_(m)} are QAM symbols normalized to have unitaverage energy and let x=[x₁, x₂, . . . , x_(M)]^(T)=Fs, where F is theM×M DFT matrix.

We obtain{circumflex over (x)} _(m) =h _(m) ^(†) R _(m) ⁻¹ y _(m) , m=1, . . . ,M.  (17)Defining {circumflex over (x)}=[{circumflex over (x)}₁, . . . ,{circumflex over (x)}_(M)]^(T) and applying the inverse DFT on{circumflex over (x)}, we obtain

$\begin{matrix}{\hat{s} = {\left\lbrack {{\hat{s}}_{1},\ldots\mspace{14mu},{\hat{s}}_{M}} \right\rbrack^{T}\overset{\bigtriangleup}{=}{F^{\dagger}{\hat{x}.}}}} & (18)\end{matrix}$

Suppose we form the pair ŝ_(m,q)=[ŝ_(m), ŝ_([m+q])]^(T) for any given q:1≦q≦M−1 and where [m+q]=(m+q−1)mod(M)+1. Please note that the pairingemployed in OFDMA before always uses q=1. Then we determine the matrixX(q) such that

$\begin{matrix}{{{I - {X(q)}} = {\frac{1}{M}\left\lbrack \begin{matrix}{\sum\limits_{k = 1}^{M}{h_{k}^{\dagger}R_{k}^{- 1}h_{k}}} & \begin{matrix}{\sum\limits_{k = 1}^{M}{h_{k}^{\dagger}R_{k}^{- 1}h_{k}\exp}} \\\left( {j\; 2\pi\;{{q\left( {k - 1} \right)}/M}} \right)\end{matrix} \\\begin{matrix}{\sum\limits_{k = 1}^{M}{h_{k}^{\dagger}R_{k}^{- 1}h_{k}^{(1)}\exp}} \\\left( {j\; 2\pi\;{{q\left( {k - 1} \right)}/M}} \right)\end{matrix} & {\sum\limits_{k = 1}^{M}{h_{k}^{\dagger}R_{k}^{- 1}h_{k}}}\end{matrix} \right\rbrack}}} & (19)\end{matrix}$Next, we compute the 2×2 matrix Q(q)ε

^(2×2) using the Cholesky decompositionQ(q)Q(q)^(\)=(I−X(q))X(q)  (20)and then determine

${z_{m,q}\overset{\Delta}{=}{{Q(q)}^{- 1}{\hat{s}}_{m,q}}},$1≦m≦M. z_(m,q)ε

^(2×1) permits the expansion

$\begin{matrix}{{z_{m,q} = {{\underset{\underset{T{(q)}}{︸}}{{Q(q)}^{- 1}\left( {I - {X(q)}} \right)}s_{m,q}} + {\overset{˘}{n}}_{m,q}}},} & (21)\end{matrix}$with T(q)ε

^(2×2), s_(m,q)=[s_(m), s_([m+q])]^(T) and

[{hacek over (n)}_(m,q){hacek over (n)}_(m,q) ^(†)]=I. The two symbolsin s_(m,q) can now be jointly demodulated using the two-symbol max-logdemodulator on z_(m,q).

To determine the best q (or equivalently the best pair (m, [m+q])) wecan use the capacity metric on the model in (21) and determine asuitable q as

$\begin{matrix}\begin{matrix}{{\arg\;{\max\limits_{1 \leq q \leq {M/2}}{\det\;\left( {I + {{T(q)}^{\dagger}{T(q)}}} \right)}}} = {\arg{\max\limits_{1 \leq q \leq {M/2}}{\det\left( {X(q)}^{- 1} \right)}}}} \\{{= {\arg{\min\limits_{1 \leq q \leq {M/2}}{{\det\left( {X(q)} \right)}.}}}}\;}\end{matrix} & (22)\end{matrix}$Thus, we can equivalently first determine the (first M/2+1 rows of the)vectorr=F[h ₁ ^(†) R ₁ ⁻¹ h ₁ , . . . , h _(M) ^(†) R _(M) ⁻¹ h_(M)]^(T)  (23)and compute {circumflex over (q)} as

$\begin{matrix}{\hat{q} = {{\arg\;{\max\limits_{2 \leq k \leq {{M/2} + 1}}\left\{ {r_{k}} \right\}}} - 1.}} & (24)\end{matrix}$

Referring again to the diagram of FIG. 3, for the case of demodulating asingle signal codeword, the input to the linear minimum mean squareerror equalizer LMMSE 100 is a signal vector of the formy_(m)=h_(m)x_(m)+n_(m) (16). The output (17) from the equalizer 100,according to the form {circumflex over (x)}_(m)=h_(m) ^(†)R_(m) ⁻¹y_(m),m=1, . . . , M (17), is them handled by the M-point inverse discreteFourier Transform processing 102 to provide a transformed output of theform

$\begin{matrix}{\hat{s} = {\left\lbrack {{\hat{s}}_{1},\ldots\mspace{14mu},{\hat{s}}_{M}} \right\rbrack^{T}\overset{\Delta}{=}{F^{\dagger}{\hat{x}.}}}} & (18)\end{matrix}$This output from the IDFT circuit is then handled by a pairing andwhitening processing 104 which outputs either the IDFT output accordingto (18) or

$z_{m,q} = {{\underset{\underset{T{(q)}}{︸}}{{Q(q)}^{- 1}\left( {I - {X(q)}} \right)}s_{m,q}} + {{\overset{˘}{n}}_{m,q}\mspace{14mu}{according}\mspace{14mu}{to}\mspace{14mu}{(21).}}}$

Based on the channel estimates and the data rate, the pairing andwhitening module 104 can decide whether or not to process its inputsignal. In case the pairing and whitening module decides not to processits input signal, then the input to the calculator 106 is of the form(18) and SISO LLR calculator is used in 106. In case the pairing andwhitening module 104 decides to process its input signal, then theoutput of the pairing and whitening module consists of length-2 vectorsof the form (21) and the Two-symbol MLSD function in the calculator 106is used. An illustrative pairing and whitening procedure is given by thefollowing relationships

$\begin{matrix}{{r = {F\left\lbrack {{h_{1}^{\dagger}R_{1}^{- 1}h_{1}},\ldots\mspace{14mu},{h_{M}^{\dagger}R_{M}^{- 1}h_{M}}} \right\rbrack}^{T}}\mspace{14mu}} & (23) \\{{{{and}\mspace{14mu}\hat{q}} = {{\arg\;{\max\limits_{2 \leq k \leq {{M/2} + 1}}\left\{ {r_{k}} \right\}}} - 1.}},} & (24)\end{matrix}$described in detail above.

Referring again to the diagram of FIG. 4, for the case of demodulatingmultiple signal codewords, the input to the LMMSE equalizers 200 (202)is a signal vector of the form y_(m)=H_(m)x_(m)+n_(m) (1). The output ofthe LMMSE equalizers 200 (202) and input to inverse discrete Fouriertransformers IDFT 204 (206) is of the form

$\begin{matrix}{{\begin{bmatrix}{\hat{x}}_{m}^{(1)} \\{\hat{x}}_{m}^{(2)}\end{bmatrix} = {{{H_{m}^{\dagger}\left( {I + {H_{m}H_{m}^{\dagger}}} \right)}^{- 1}y_{m}} = {\left( {I + {H_{m}^{\dagger}H_{m}}} \right)^{- 1}H_{m}^{\dagger}y_{m}}}},{m = 1},\ldots\mspace{14mu},{M.}} & (3)\end{matrix}$The output of inverse DFTs 204 (206) and input to the pairing andwhitening module 208 is of the form

$\begin{matrix}{{\hat{s}}^{(k)}\overset{\Delta}{=}{F^{\dagger}{{\hat{x}}^{(k)}.}}} & (4)\end{matrix}$The output of the pairing and whitening module 208 is either of the formin (4) or in (12).

Based on the channel estimates and the data rate, the pairing andwhitening module 208 can decide whether or not to process its inputsignal. In case it decides not to process its input signal, then theinput to the calculator 210 is of the form (4) and SISO LLR calculatoris used in 210. In case module 208 decides to process its input, theoutput of module 208 is produced using a pairing and whitening procedureand consists of length-2 vectors of the form in (12). An illustrativepairing and whitening procedure is given by

$\begin{matrix}{r = {F\left\lbrack {{{h_{1}^{(1)}}^{\dagger}R_{1}^{- 1}h_{1}^{(2)}},\ldots\mspace{14mu},{{h_{M}^{(1)}}^{\dagger}R_{M}^{- 1}h_{M}^{(2)}}} \right\rbrack}^{T}} & (14) \\{{{{and}\mspace{14mu}\hat{q}} = {{\arg\;{\max\limits_{1 \leq k \leq M}\left\{ {r_{k}} \right\}}} - 1}},} & (15)\end{matrix}$which is described in detail above.

The present invention has been shown and described in what areconsidered to be the most practical and preferred embodiments. It isanticipated, however, that departures may be made therefrom and thatobvious modifications will be implemented by those skilled in the art.It will be appreciated that those skilled in the art will be able todevise numerous arrangements and variations, which although notexplicitly shown or described herein, embody the principles of theinvention and are within their spirit and scope.

What is claimed is:
 1. A receiver for discrete Fouriertransform-spread-orthogonal frequency division multiplexing (DFT-S-OFDM)based systems, comprising: a prefilter for demodulating one of areceived signal codeword and received signal codewords; and alog-likelihood ratio LLR module responsive to the prefilter, wherein theprefilter includes a pairing and whitening module that, based on channelestimates and a data rate, enables the LLR module to perform either aSerial-In-Serial-Out (SISO) based log likelihood ratio processing of anoutput from the pairing and whitening module or a two-symbol max-logsoft output demodulator (two-symbol MLSD) based log likelihood ratioprocessing of the output from the pairing and whitening module, thepairing and whitening module electing not to process an input receivedfrom an inverse discrete Fourier transform (IDFT) module when the LLRmodule is enabled to perform the SISO based log likelihood ratioprocessing.
 2. The receiver of claim 1, wherein the pairing andwhitening module provides an output of the form${\hat{s} = {\left\lbrack {{\hat{s}}_{1},\ldots\mspace{14mu},{\hat{s}}_{M}} \right\rbrack^{T}\overset{\Delta}{=}{F^{\dagger}\hat{x}}}},$where {circumflex over (x)} is a per-tone equalized received signalvector in the frequency domain and F^(†) performs an inverse discreteFourier transform (IDFT) operation on an M×M matrix.
 3. The receiver ofclaim 1, wherein for received signal codewords the pairing and whiteningmodule provides an output of the form${{\hat{s}}^{(k)}\overset{\Delta}{=}{F^{\dagger}{\hat{x}}^{(k)}}},$where {circumflex over (x)}^((k)) is a per-tone equalized receivedsignal vector in the frequency domain corresponding to the k^(th)codeword and F^(\) performs an inverse discrete fourier transform (IDFT)operation.
 4. The receiver of claim 1, wherein for received signalcodewords the pairing procedure is consistent with the following signalrelationshipsr=F[h ₁ ^((1)†) R ₁ ⁻¹ h ₁ ⁽²⁾ , . . . , h _(M) ^((1)†) R _(M) ⁻¹ h _(M)⁽²⁾]^(T) and compute {circumflex over (q)} as${\hat{q} = {{\arg\;{\max\limits_{1 \leq k \leq M}\left\{ {r_{k}} \right\}}} - 1}},$where h_(m) ⁽¹⁾, h_(m) ⁽²⁾ denote the frequency domain channel responsevectors on an m^(th) tone corresponding to codeword 1 and codeword 2,respectively, and R_(m) denotes a covariance matrix for the m^(th) toneand F denotes a discrete Fourier transform matrix, {circumflex over (q)}being determined by subtracting one from an index of a maximum magnitudeelement of the vector r, an m^(th) symbol of codeword 1 being pairedwith an (m+{circumflex over (q)})^(th) symbol of codeword 2 subject to amodulo operation.
 5. A receiver for discrete Fouriertransform-spread-orthogonal frequency division multiplexing (DFT-S-OFDM)based systems, comprising: a prefilter for demodulating one of areceived signal codeword and received signal codewords; and alog-likelihood ratio LLR module responsive to the prefilter, wherein theprefilter includes a pairing and whitening module that, based on channelestimates and a data rate, enables the LLR module to perform either aSerial-In-Serial-Out (SISO) based log likelihood ratio processing of anoutput from the pairing and whitening module or a two-symbol max-logsoft output demodulator (two-symbol MLSD) based log likelihood ratioprocessing of the output from the pairing and whitening module, thepairing and whitening module electing to process an input received froman inverse discrete Fourier transform (IDFT) module when the LLR moduleis enabled to perform the two-symbol MLSD based log likelihood ratioprocessing.
 6. The receiver of claim 5, wherein the pairing andwhitening module divides the symbols of a same codeword into multiplepairs and obtains a decision vector and an effective channel matrix foreach pair.
 7. The receiver of claim 5, wherein the pairing and whiteningmodule divides the symbols of two different codewords into multiplepairs and obtains a decision vector and an effective channel matrix foreach pair.
 8. The receivers of claim 6, wherein LLRs corresponding tocoded bits in each symbol pair are computed by the two-symbol MLSDresponsive to the decision vector and the effective channel matrix ofthat pair.
 9. The receiver of claim 6, wherein the pairing and whiteningmodule provides an output consisting of length-2 decision vectors{z_(m)} that are expanded as z_(m)=T_(m)s_(m)+{hacek over (n)}_(m),where s_(m) denotes the vector consisting of the m^(th) pair of symbolsfrom the same codeword and T_(m) denotes the effective channel matrixfor the m^(th) pair obtained after pairing and noise whitening with{hacek over (n)}_(m) being the whitened noise vector having twouncorrelated elements.
 10. The receiver of claim 7, wherein for multiplereceived signal codewords, the pairing and whitening module provides anoutput consisting of length-2 decision vectors {z_(m)} that are expandedas z_(m)=T_(m)s_(m)+{hacek over (n)}_(m), where s_(m) denotes the vectorconsisting of the m^(th) pair of symbols from two different codewordsand T_(m) denotes the effective channel matrix for the m^(th) pairobtained after pairing and noise whitening with {hacek over (n)}_(m)being the whitened noise vector having two uncorrelated elements. 11.The receiver of claim 9, wherein the pairing and whitening moduleprovides an output consisting of length-2 decision vectors {z_(m)} thatare expanded as z_(m)=Ts_(m)+{hacek over (n)}_(m), where s_(m) denotesthe vector consisting of the m^(th) pair of symbols from the samecodeword and T denotes the effective channel matrix which is identicalfor all pairs with {hacek over (n)}_(m) being the whitened noise vectorhaving two uncorrelated elements.
 12. The receiver of claim 10, whereinthe pairing and whitening module provides an output consisting oflength-2 decision vectors {z_(m)} that are expanded asz_(m)=Ts_(m)+{hacek over (n)}_(m), where s_(m) denotes the vectorconsisting of the m^(th) pair of symbols from two different codewordsand T denotes the effective channel matrix which is identical for allpairs with {hacek over (n)}_(m) being the whitened noise vector havingtwo uncorrelated elements.
 13. The receiver of claim 5, wherein apairing procedure is consistent with the following signal relationshipsr=F[h ₁ ^(†) R ₁ ⁻¹ h ₁ , . . . , h _(M) ^(†) R _(M) ⁻¹ h _(M)]^(T) andcompute {circumflex over (q)} as${\hat{q} = {{\arg\;{\max\limits_{2 \leq k \leq {{M/2} + 1}}\left\{ {r_{k}} \right\}}} - 1}},$where h_(m) denotes the frequency domain channel response vector on anm^(th) tone, R_(m) denotes a covariance matrix for the m^(th) tone and Fdenotes a discrete Fourier transform matrix, {circumflex over (q)} beingdetermined by subtracting 1 from the index of the element of the vectorr that among all the elements of the vector r with indices in {2, . . ., M/2+1} has the maximum magnitude, and an m^(th) symbol of the codewordbeing then paired with an (m+{circumflex over (q)})^(th) symbol of asame codeword.
 14. A receiver for discrete Fouriertransform-spread-orthogonal frequency division multiplexing (DFT-S-OFDM)based systems, comprising: a prefilter for demodulating one of areceived signal codeword and received signal codewords; and alog-likelihood ratio LLR module responsive to the prefilter, wherein theprefilter includes a pairing and whitening module that, based on channelestimates and a data rate, enables the LLR module to perform either aSerial-In-Serial-Out (SISO) based log likelihood ratio processing of anoutput from the pairing and whitening module or a two-symbol max-logsoft output demodulator (two-symbol MLSD) based log likelihood ratioprocessing of the output from the pairing and whitening module, theprefilter including a per-tone equalizer for one of the received signalcodeword and received signal codewords and an inverse discrete Fouriertransform IDFT module responsive to the equalizer, the pairing andwhitening module being responsive to the IDFT module.